Announcements - 9 Oct 2014

Transcription

1 Announcements - 9 Oct Prayer 2. Exam 2 results a. Median Score: b. Curve: c. Exams will be returned soon, our office assistant should put them in the boxes near N357 ESC sometime today. d. I'll post my solutions to the class website soon (probably this afternoon) 3. If you have questions about the exam that you'd like to discuss with me: a. Please look over your own exam & the posted solutions to figure things out as best you can, before coming to talk to me. b. Talking to me during my office hours is best c. Individual appointments can also be made Colton Lecture 12 - pg 1

2 Which of the problems from last night's HW assignment would you most like me to discuss in class today? Colton Lecture 12 - pg 2

3 Momentum Review Equations Definition: p mv Conservation Law (blueprint): p p before after (if no. ) From warmup To solve 2-dimensional collision problems, you should: a. treat momentum as a vector b. treat momentum as a scalar Colton Lecture 12 - pg 3

4 Worked Problem Three carts collide on an air track. Carts m 1 and m 3 have the same mass, and m 2 has twice the mass. The initial velocities are 1.5 m/s, 1 m/s, and -1 m/s. The three stick together. What is the combined velocity after the collision? (magnitude and direction) Answer: m/s, to the right Colton Lecture 12 - pg 4

5 Limitation Like conservation of energy, conservation of momentum is a before and after law which doesn t tell you about: If you want to know about, you have to know Colton Lecture 12 - pg 5

6 Impulse Concept: A force exerted for a brief time causes a change in momentum The "impulse" is the force time. F t p Impulse equation (focusing on one object) Derivation: F ma v F m t F t m v F t p F When to use? Colton Lecture 12 - pg 6

7 Worked Problem Two steel balls (same mass, m = kg) bounce off of each other. High speed photography reveals that the two balls are in contact for s. Before the collision, the left ball is traveling to the right at 2 m/s and the right ball is traveling to the left at 2 m/s. After the collision, the left ball is traveling to the left, still at 2 m/s, and the right ball is traveling to the right at 2 m/s. What was the contact force during the collision? Answer: N Colton Lecture 12 - pg 7

8 From last lecture's warmup, do as clicker quiz A ping-pong ball moving forward with a momentum p strikes and bounces off backwards from a heavier tennis ball that is initially at rest and free to move. The tennis ball is set in motion with a momentum: a. greater than p b. less than p c. equal to p What about if ping-pong ball thuds and falls flat? Demo: Elastic and Inelastic Pendulum which will cause the wood to be knocked over? Colton Lecture 12 - pg 8

9 Question Is energy conserved in collisions? All? Some? None? Colton Lecture 12 - pg 9

10 Special Case: Elastic Collisions In some special collisions, energy is also conserved! Elastic collisions: no lost kinetic energy they are bouncy Inelastic collisions: (but not all bouncy-looking collisions are elastic don t assume) Perfectly inelastic collisions: Colton Lecture 12 - pg 10

11 From warmup In addition to momentum, kinetic energy is also typically conserved in collisions. a. true b. false Colton Lecture 12 - pg 11

12 Elastic Collisions KE before = KE after This is in addition to p before p after The two equations can be put together to give: v v v v after 1 2 before 2 1 "velocity reversal equation" Colton Lecture 12 - pg 12

13 Derivation of velocity reversal equation Cons. mom Cons. energy mv mv mv mv 1 1i 2 2i 1 1f 2 2f i f f i m 1 v 1 i v 1 f m 2 v 2 f v 2 i m1 v1 i v1f v1i v1f m2 v2f v2i v2f v2i m v v m v v mv 2 1 1i mv 2 2 2i mv 2 1 1f mv 2 2 2f Divide the two equations. m 1 v1 i v1f v1 i v1f m 1 v1 i v1f m 2 v 2f v2i v2f v2i m 2 v2f v2i v v v v 1i 1f 2f 2i v v v v 1i 2i 2f 1f Colton Lecture 12 - pg 13

14 Dr. Colton s guide, cont. #7. If it s a 1D elastic collision then in addition to conservation of momentum, also use v v v v after 1 2 before 2 1 "velocity reversal equation" Careful with signs! Right = positive, left = negative applies Colton Lecture 12 - pg 14

15 From warmup Ralph is confused. He's looking at what I call the "velocity reversal equation" in the book. The textbook says "This equation, in combination with conservation of momentum, will be used to solve problems dealing with perfectly elastic head-on collisions." What confuses Ralph, is why won't we need to use the conservation of energy equation? Shouldn't energy conservation be important in elastic collisions? Help him understand why we don't use this: mv mv mv mv i 2 2i 1 1f 2 2f Think-pair-share Think about it for a bit Talk to your neighbor, find out if he/she thinks the same as you Be prepared to share your answer with the class if called on Clicker: I am now ready to share my answer if randomly selected. a. Yes Note: you are allowed to "pass" if you would really not answer. Colton Lecture 12 - pg 15

16 Demo Problem A cart moving at 1 m/s bounces elastically off of a second cart of twice the mass which is moving at 0.5 m/s in the same direction. What velocity does each cart now have? Answer: v 1 = m/s; v 2 = m/s Colton Lecture 12 - pg 16

17 Demo Problem A cart moving at 1 m/s bounces elastically off of a second cart of the same mass which is stationary. What velocity does each cart now have? Demo: Newton s cradle Colton Lecture 12 - pg 17

18 Worked problem Elastic collision between big M and small m, bowling ball vs. marble 15 g, 3 m/s 5 kg, 3 m/s What are the final speeds? Hint: v bowling ball final v bowling ball initial. Use only velocity reversal eqn. Answer: v marble = 9 m/s Colton Lecture 12 - pg 18

19 Demo Velocity amplifier Colton Lecture 12 - pg 19

20 Multi-step problems Collision followed by something else Ballistic pendulum. A bullet of mass m and speed v embeds in a block of wood of mass M hanging from a string. How high do they rise? 1 mv m M gh 2 2 How not to do: How to do: 1. Collision part: p is conserved (but KE is not!) i. This gets you the velocity right after the collision 2. Motion part: Energy is conserved (but p is not!) i. This gets you the height based on velocity Colton Lecture 12 - pg 20

21 Before After/Before After Answer: 2 2 m v h m M 2g Colton Lecture 12 - pg 21

22 HW 13-1: Very similar! Colton Lecture 12 - pg 22

23 Explosions Is momentum conserved? What is the center of mass? How does the center of mass move? Colton Lecture 12 - pg 23

24 Center of Mass Demo: Foam object Demo: Spring apart gliders Colton Lecture 12 - pg 24

25 Worked Problem An artillery shell of mass 20 kg is moving east at 100 m/s. It explodes into two pieces. One piece (mass 12 kg) is seen moving north at 50 m/s. What is the velocity (magnitude and direction) of the other piece? Answers: v x = 250 m/s; v y = -75 m/s; v = 261 m/s at 16.7 south of east Colton Lecture 12 - pg 25